Biomedical subjects

Natalia L Komarova

Publications and source records attributed to Natalia L Komarova.

At least 19 recordsLinked to original sources

PubMed2006

Epithelial tissue architecture protects against cancer.

We consider the design of colon crypts from the point of view of minimizing the likelihood of generation of cancerous mutations. A stochastic mathematical model (a finite branching process) is developed and fully analyzed. It is found that depending on the mutation rates, different designs are evolutionarily advantageous. If the mutation rates associated with stem cells are a lot higher than the mutation rates of daughter cells, then few stem cells per crypt is the evolutionarily optimal strategy. If the mutation rates of stem cells are of the same order of magnitude or lower than those for daughter cells, then having as many stem cells per crypt as possible is the desirable design. We also found that the optimal evolutionary strategy may work very well to protect the organism from cancer in the young age, but the same strategy becomes detrimental as the organism ages. It pushes the onset of cancer back in time, but it results in an elevated cancer initiation rates as the organism gets older. Our model quantifies the idea that cancer and aging are the two sides of one coin.

Adenomatous Polyposis Coli Protein↗

PubMed2006

Spatial stochastic models for cancer initiation and progression.

The multistage carcinogenesis hypothesis has been formulated by a number of authors as a stochastic process. However, most previous models assumed "perfect mixing" in the population of cells, and included no information about spatial locations. In this work, we studied the role of spatial dynamics in carcinogenesis. We formulated a 1D spatial generalization of a constant population (Moran) birth-death process, and described the dynamics analytically. We found that in the spatial model, the probability of fixation of advantageous and disadvantageous mutants is lower, and the rate of generation of double-hit mutants (the so-called tunneling rate) is higher, compared to those for the space-free model. This means that the results previously obtained for space-free models give an underestimation for rates of cancer initiation in the case where the first event is the generation of a double-hit mutant, e.g. the inactivation of a tumor-suppressor gene.

Algorithms↗

PubMed2005

A theoretical framework for specificity in cell signaling.

Different cellular signal transduction pathways are often interconnected, so that the potential for undesirable crosstalk between pathways exists. Nevertheless, signaling networks have evolved that maintain specificity from signal to cellular response. Here, we develop a framework for the analysis of networks containing two or more interconnected signaling pathways. We define two properties, specificity and fidelity, that all pathways in a network must possess in order to avoid paradoxical situations where one pathway activates another pathway's output, or responds to another pathway's input, more than its own. In unembellished networks that share components, it is impossible for all pathways to have both mutual specificity and mutual fidelity. However, inclusion of either of two related insulating mechanisms--compartmentalization or the action of a scaffold protein--allows both properties to be achieved, provided deactivation rates are fast compared to exchange rates.

Algorithms↗

PubMed2005

On the role of endothelial progenitor cells in tumor neovascularization.

The exact role that bone marrow (BM)-derived endothelial progenitor cells (EPCs) play in tumor neovascularization is heavily debated. We develop a quantitative three-compartment model with predictive power regarding the dynamics of tumorigenesis. There are two distinct processes by which tumor neovasculature can be built: angiogenesis is the formation of new blood vessels from preexisting vessels; vasculogenesis is the formation of new vessels by recruiting circulating EPCs. We show that vasculogenesis-driven and angiogenesis-driven tumors grow in different ways. (i) If angiogenesis is the prevailing process, then the tumor mass (and volume) will grow as a cubic power of time, and BM-derived EPCs will stay at a constant level. (ii) If vasculogenesis is the dominant process, then the tumor mass will be characterized by a linear growth in time, and the number of circulating EPCs (after possibly increasing to a maximum) will decrease to low levels. With this information, one can identify the "signature" of each of the processes in the observations of tumor growth and the dynamics of the relevant characteristics, such as the level of BM-derived EPCs. We show how our results can help explain some apparently contradictory experimental data. We also propose ways to couple this study with directed experiments to identify the exact role of vasculogenesis in tumor progression.

Blood Vessels↗

PubMed2005

Drug resistance in cancer: principles of emergence and prevention.

Although targeted therapy is yielding promising results in the treatment of specific cancers, drug resistance poses a problem. We develop a mathematical framework that can be used to study the principles underlying the emergence and prevention of resistance in cancers treated with targeted small-molecule drugs. We consider a stochastic dynamical system based on measurable parameters, such as the turnover rate of tumor cells and the rate at which resistant mutants are generated. We find that resistance arises mainly before the start of treatment and, for cancers with high turnover rates, combination therapy is less likely to yield an advantage over single-drug therapy. We apply the mathematical framework to chronic myeloid leukemia. Early-stage chronic myeloid leukemia was the first case to be treated successfully with a targeted drug, imatinib (Novartis, Basel). This drug specifically inhibits the BCR-ABL oncogene, which is required for progression. Although drug resistance prevents successful treatment at later stages of the disease, our calculations suggest that, within the model assumptions, a combination of three targeted drugs with different specificities might overcome the problem of resistance.

Antineoplastic Agents↗

PubMed2005

Nonlinear waves in double-stranded DNA.

We propose a nonlinear model derived from first principles, to describe bubble dynamics of DNA. Our model equations include a term derived from the dissipative effect of intermolecular vibrational modes. Such modes are excited by the propagating bubble, and we term this 'curvature dissipation'. The equations that we derive allow for stable pinned localized kinks which form the bubble. We perform the stability analysis and specify the energy requirements for the motion of the localized solutions. Our findings are consistent with properties of DNA dynamics, and can be used in models for denaturation bubbles, RNA and DNA transcription, nucleotide excision repair and meiotic recombination.

DNA↗

PubMed2005

Emergence and prevention of resistance against small molecule inhibitors.

Small molecule inhibitors target specific metabolic pathways in tumor cells and are a promising class of drugs for the treatment of cancers. The best known example is the treatment of chronic myeloid leukemia (CML) with Gleevec. This is a small molecule inhibitor of the Bcr-Abl kinase which has been shown to drive the initiation and progression of CML. While treatment of early stage CML with Gleevec has been quite successful, later stages of the disease (blast crisis) are not successfully treated due to the emergence of drug resistant cells. It is therefore important to understand the principles according to which drug resistant cells evolve, so that we can design treatment strategies which aim to prevent the rise of resistant cells. Such evolutionary dynamics can be studied with mathematical models, and this article reviews such an approach. We address three specific questions: (i) Do resistant cells emerge before or after the start of therapy? (ii) How does the turnover rate of cancer cells influence the evolution of drug resistant cells? (iii) Can combination therapy be used to prevent drug resistance? We apply our model to the treatment of CML with Gleevec, in order to demonstrate how this mathematical framework can be applied to the treatment of a specific cancer with small molecule inhibitors.

Antineoplastic Agents↗

PubMed2005

Cancer, aging and the optimal tissue design.

Division patterns or mammalian tissues, like every other feature of life, have been subject to evolutionary pressures throughout the natural history. A particular and very important design principle that we discuss in this paper is the protective role of tissue architecture against cancer. We present a stochastic dynamical model of cell renewal of epithelial tissue (colonic crypts) which explicitly includes asymmetric indefinite divisions of stem cells and symmetric, finite divisions of daughter cells. We find that the hierarchical structure of crypts plays a protective role against accumulation of double-mutants. We argue that daughter cells, and not only stem cells, can play a role in carcinogenesis. Our model also predicts the optimum number of stem cells per crypt. In most cases, higher numbers of stem cells per crypt correspond to lowering the chance of colon cancer initiation (except if mutation rates associated with daughter cells are a lot lower than those associated with stem cells). Finally, we argue that the evolutionarily optimum which corresponds to a large number of stem cells per crypt, pushes the onset of cancer to an older age, but it actually acts against older individuals by increasing their chance of developing cancer.

Aging↗

PubMed2005

Mathematical modeling of tumorigenesis: mission possible.

PURPOSE OF REVIEW: Mathematical modeling of tumorigenesis is a fast-growing area of research. This review describes recent (since July 2003) advances in this area and discusses possible implications for the field of cancer biology in general. RECENT FINDINGS: Broadly speaking, there are three major areas in which theory has contributed the most to cancer research: (1) modeling in the context of epidemiology and other statistical data, (2) mechanistic modeling of avascular and vascular tumor growth, and (3) modeling of cancer initiation and progression as somatic evolution. The first area uses models to fit the existing data, the second approach takes advantage of methods of physics and engineering to describe tumor growth, and the third method looks at cancer progression as a local, Darwinian evolution. SUMMARY: The article describes new, interesting ideas put forward in the last year, and suggests that to make the modeling effort more relevant, a better dialogue should be developed between theorists and experimental biologists. The author believes this is possible.

Aging↗

PubMed2004

Initiation of colorectal cancer: where do the two hits hit?

It is widely believed that stem cells are of special importance for colorectal cancer initiation. The earliest event being the inactivation of both alleles of the Adenomatous Polyposis Coli (APC) gene, it is thought that the stem cells are the most likely target for these two first hits. Indeed, at the first glance, short-lived differentiated cells cannot sustain a mutation long enough for the second hit to occur, because of the constant apoptosis/renewal process in epithelial tissues. Using a straightforward calculation, we show that this intuitive argument is incorrect. Our model based on the conventional view of colon crypt architecture, suggests that at least one of the two hits may occur in the migrating compartment. We suggest that a possible role of differentiating cells in cancer initiation cannot be discarded simply based on the fact that they are short-lived. More evidence is needed to understand the cellular origins of cancer and to identify whether or not a double hit in a daughter cell can be "immortalizing". In this study we discuss several scenarios and propose some experiments which can shed light on these questions.

Cell Differentiation↗

PubMed2004

Population genetics of tumor suppressor genes.

Cancer emerges when a single cell receives multiple mutations. For example, the inactivation of both alleles of a tumor suppressor gene (TSG) can imply a net reproductive advantage of the cell and might lead to clonal expansion. In this paper, we calculate the probability as a function of time that a population of cells has generated at least one cell with two inactivated alleles of a TSG. Different kinetic laws hold for small and large populations. The inactivation of the first allele can either be neutral or lead to a selective advantage or disadvantage. The inactivation of the first and of the second allele can occur at equal or different rates. Our calculations provide insights into basic aspects of population genetics determining cancer initiation and progression.

Alleles↗

PubMed2004

On the emergence of multifocal cancers.

Several tumors can exist as multiple lesions within a tissue. The lesions may either arise independently, or they may be monoclonal. The importance of multiple lesions for tumor staging, progression, and treatment is subject to debate. Here we use mathematical models to analyze the emergence of multiple, clonally related lesions within a single tissue. We refer to them as multi-focal cancers. We find that multifocal cancers can arise through a dynamical interplay between tumor promoting and inhibiting factors. This requires that tumor promoters act locally, while tumor inhibitors act over a longer range. An example of such factors may be angiogenesis promoters and inhibitors. The model further suggests that multifocal cancers represent an intermediate stage in cancer progression as the tumor evolves away from inhibition and towards promotion. Different patterns of progression can be distinguished: (i) If tumor inhibition is strong, the initial growth occurs as a unifocal and self contained lesion; progression occurs through bifurcation of the lesion and this gives rise to multiple lesions. As the tumor continues to evolve and pushes the balance between inhibition and promotion further towards promotion, the multiple lesions eventually give rise to a single large mass which can invade the entire tissue. (ii) If tumor inhibition is weaker upon initiation, growth can occur as a single lesion without the occurrence of multiple lesions, until the entire tissue is invaded. The model suggests that the sum of the tumor sizes across all lesions is the best characteristic which correlates with the stage and metastatic potential of the tumor.

Journal Article↗

PubMed2004

Replicator-mutator equation, universality property and population dynamics of learning.

Replicator-mutator equation is used to describe the dynamics of complex adaptive systems in population genetics, biochemistry and models of language learning. We study "localized", or "coherent", solutions, which are especially relevant in the context of learning and correspond to the existence of a predominant language in the population. There is a coherence threshold for learning fidelity, above which coherent communication can be maintained. We prove the following surprising universality property of coherence threshold: for typical realizations of random coefficients in the fitness matrix, the value of the coherence threshold does not depend on the size of the system.

Biological Evolution↗

PubMed2004

Genomic instability in cancer: biological and mathematical approaches.

Genomic instability occurs in a majority of cancers. It manifests itself in a large number genetic alterations in cancer cells, such as small scale mutations, losses and gains of whole chromosomes and parts of chromosomes and mitotic recombinations. The role of genomic instability is still unknown. It is difficult to study because of its heterogeneous nature. Most methods based on looking for defined features of genes or gene expressions, are not applicable for unstable populations of cells. A variety of approaches are used to study genomic instability. These include experimental studies of cancer cell lines and mouse models, analysis of large amounts of data on loss of heterozygocity, and mathematical modeling of the relevant processes. We describe these approaches here; integration of different methods can improve our understanding of genomic instability.

Aging↗

PubMed2004

Evolutionary dynamics of tumor suppressor gene inactivation.

Tumor suppressor genes (TSGs) are important gatekeepers that protect against somatic evolution of cancer. Losing both alleles of a TSG in a single cell represents a step toward cancer. We study how the kinetics of TSG inactivation depends on the population size of cells and the mutation rates for the first and second hit. We calculate the probability as function of time that at least one cell has been generated with two inactivated alleles of a TSG. We find three different kinetic laws: in small, intermediate, and large populations, it takes, respectively, two, one, and zero rate-limiting steps to inactivate a TSG. We also study the effect of chromosomal and other genetic instabilities. Small lesions without genetic instability can take a very long time to inactivate the next TSG, whereas the same lesions with genetic instability pose a much greater risk for cancer progression.

Alleles↗

PubMed2004

The optimal rate of chromosome loss for the inactivation of tumor suppressor genes in cancer.

Many cancers are characterized by chromosomal instability (CIN). This phenotype involves the deletion and duplication of chromosomes or chromosome parts and results in a high degree of aneuploidy. The role of CIN for cancer progression is a very important, yet unresolved question. It has been argued that CIN contributes to cancer initiation because chromosome loss can unmask a mutated tumor suppressor (TSP) gene. At the same time, CIN is costly for the cell because it destroys the genome and therefore compromises clonal expansion. Here, we use mathematical models to determine whether CIN can accelerate the generation and expansion of TSP(-/-) cells in the context of this tradeoff. Comparing cells with different degrees of CIN, we find that the emergence and growth of TSP(-/-) cells is optimized if the rate of chromosome loss is of the order of 10(-3) to 10(-2). This result is very robust, is independent of parameter values, and coincides with experimental measures using colon cancer cell lines. However, if we consider all of the steps in the pathway, including the generation of the CIN phenotype from stable cells, then it turns out that the emergence and growth of TSP(-/-) cells is never accelerated by CIN. Therefore, CIN does not arise because it accelerates the accumulation of adaptive mutations. Instead, it arises for other reasons, such as environmental factors, and is subsequently fine-tuned by selection to minimize the time to further cancer progression by means of the inactivation of TSP genes.

Animals↗

PubMed2003

Evolutionary dynamics of mutator phenotypes in cancer: implications for chemotherapy.

Genetic instability is a central characteristic of cancers. However, the selective forces responsible for the emergence of genetic instability are not clear. We use mathematical models to determine the conditions under which selection favors instability, and when stable cells are advantageous. We take into account the processes of DNA damage, repair, cell cycle arrest, mutation, and death. We find that the rate of DNA damage can play a major role in this context. In particular, an increase in the rate of DNA damage can reverse the relative fitness of stable and unstable cells. In terms of cancer progression, we find the following results. If cells have intact apoptotic responses, stable cells prevail if the DNA hit rate is low. A high DNA hit rate can result in the selection of genetically unstable cells. This has implications for the induction of tumors by carcinogens. On the other hand, if cells are characterized by impaired apoptosis, we observe the opposite. Genetic instability is selected for if the DNA hit rate is low. A high DNA hit rate can select against instability and result in the persistence of stable cells. We propose that chemotherapy can be used to reverse the relative fitness of stable and unstable cells, such that unstable cells are the inferior competitors. This could result in the competitive exclusion of progressing cancer cells.

Animals↗

PubMed2003

Mutation-selection networks of cancer initiation: tumor suppressor genes and chromosomal instability.

In this paper, we derive analytic solutions of stochastic mutation-selection networks that describe early events of cancer formation. A main assumption is that cancer is initiated in tissue compartments, where only a relatively small number of cells are at risk of mutating into cells that escape from homeostatic regulation. In this case, the evolutionary dynamics can be approximated by a low-dimensional stochastic process with a linear Kolmogorov forward equation that can be solved analytically. Most of the time, the cell population is homogeneous with respect to relevant mutations. Occasionally, such homogeneous states are connected by 'stochastic tunnels'. We give a precise analysis of the existence of tunnels and calculate the rate of tunneling. Finally, we calculate the conditions for chromosomal instability (CIN) to precede inactivation of the first tumor suppressor gene. In this case, CIN is an early event and a driving force of cancer progression. The techniques developed in this paper can be used to study arbitrarily complex mutation-selection networks of the somatic evolution of cancer.

Cell Physiological Phenomena↗